I know this is a very old story, but I have some thoughts on it I wanted to share.

Let me first share an experience that I think everybody who has ever seriously studied math (or any complicated subject) has had. You're working on a difficult math problem, say a complicated differential equation. You are certain your method is correct, but still your answer is wrong. You've checked your work, you've double checked it, you've checked it again. Your calculation seems flawless.. Finally, in desperation, you ask a friend for help. Your friend takes one glance at your work, smiles, and says: "Four times five does not equal twelve"... Oh. Yeah. Right. Good point.

We all make mistakes. Even very skilled people sometimes make elementary mistakes. Brennan in the story is doing a calculation that is very trivial for him, but it is still possible. Even if he can't see a flaw, can't even imagine a flaw, that doesn't mean the odds are zero.

Yes, they are certainly very small. Brennan is saying "The odds of me making a mistake are very small, so I am confident I am correct". But this is the Bayesian Conspiracy, not the Frequentist Conspiracy. Brennan should be asking: "Given that someone has clearly made a mistake, what are the odds of me having made it, instead of every other person in the Conspiracy. The answer is obvious.

Thus, Brennan fails as a Bayesian, and should not be accepted into the Conspiracy.

And I am not merely making a pedantic point here. This is a very important point for the real world as well. Yes, standing up to peer pressure is important, but only when it is rational. Global warning deniers also think they are standing up to peer pressure. Creationists also think they are standing up to peer pressure. And often for the exact same reason that Brennan is doing so, in this story. They thought about the issue themselves, they may even know a thing or two about it, and they really can not see any flaw in their logic, so they stick with it, convinced the odds of them having made a mistake are very small, forgetting about the huge prior.

This is actually my first post on this site. I have read quite a bit, but not everything, so I hope I am not inadvertently saying something that has been discussed before. I couldn't find anything, and I think it's an important point.